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orthonormal space

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  • Orthonormal basis — In mathematics, particularly linear algebra, an orthonormal basis for inner product space V with finite dimension is a basis for V whose vectors are orthonormal.[1][2][3] For example, the standard basis for a Euclidean space Rn is an orthonormal… …   Wikipedia

  • Orthonormal function system — An orthonormal function system (ONS) is an orthonormal basis in a vector space of functions. See basis (linear algebra), Fourier analysis, square integrable, Hilbert space for more. Categories: Mathematics stubsLinear algebraFunctional analysis …   Wikipedia

  • Orthonormal frame — In Riemannian geometry and relativity theory, an orthonormal frame is a tool for studying the structure of a differentiable manifold equipped with a metric. If M is a manifold equipped with a metric g, then an orthonormal frame at a point P of M… …   Wikipedia

  • orthonormal — adjective Date: 1932 1. of real valued functions orthogonal with the integral of the square of each function over a specified interval equal to one 2. being or composed of orthogonal elements of unit length < orthonormal basis of a vector space > …   New Collegiate Dictionary

  • orthonormal — ˌ adjective Etymology: orth + normal 1. of real valued functions : orthogonal with the integral of the square of each function over a specified interval equal to one 2. : being or composed of orthogonal elements of unit length orthonormal basis… …   Useful english dictionary

  • Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… …   Wikipedia

  • Compact operator on Hilbert space — In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite rank operators in the uniform operator topology. As such, results from matrix theory… …   Wikipedia

  • Inner product space — In mathematics, an inner product space is a vector space with the additional structure of inner product. This additional structure associates each pair of vectors in the space with a scalar quantity known as the inner product of the vectors.… …   Wikipedia

  • Minkowski space — A diagram of Minkowski space, showing only two of the three spacelike dimensions. For spacetime graphics, see Minkowski diagram. In physics and mathematics, Minkowski space or Minkowski spacetime (named after the mathematician Hermann Minkowski)… …   Wikipedia

  • Weak convergence (Hilbert space) — In mathematics, weak convergence is a type of convergence of a sequence of points in a Hilbert space (and, more generally, in a Banach space). DefinitionA sequence of points (x n) in a Hilbert space H , with n an integer, is said to converge… …   Wikipedia

  • Classifying space for U(n) — In mathematics, the classifying space for the unitary group U(n) is a space B(U(n)) together with a universal bundle E(U(n)) such that any hermitian bundle on a paracompact space X is the pull back of E by a map X → B unique up to homotopy. This… …   Wikipedia

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